122 



• KNOWLEDGE ♦ 



[Feb. 23, 1883. 



telescope, is, I believe, iniiiute<l to .Jauseii, and miH not known 

 till the end of tlio sixteenth century. Lord Bacon, in the 

 " Advancement of Learning," jiulilislicd in 1C05, speaks of it ns a 

 novel invention, and likely to assist in the investigation of the 

 minute and infinitesimal olijects of nntnrc, as, in fact, it is now 

 doing. But my puKzlo is, how did the ancient people of the earth 

 do without these aids ? or what evidence is there they possessed 

 them? Can KNowLKncK inform us ? G. G. HAKDiNGnAM. 



[I believe Mr. Foster refers to the Essay on Chaldean Astronomy 

 forming the First Appendix of my treatise on Saturn. Mention is 

 there made of a plano-convex lens discovered at Nimroud by Layard, 

 and giving a tolerably distinct focus at 4^ inches. — R. 1'.] 



A THEORY OF ATMOSPHERES. 

 [730] — 1. It is convenient to consider any atmosphere round a 

 body like the earth or sun as divided into two halves of equal 

 weight, the lower half resting on the surface of the body, under the 

 pressure of the upper half. It will be assumed that the gaseous 

 laws of volume pressure and temperature hold good, and that the 

 molecular theory is true. 



2. If the total quantity of a given atmosphere is increased or 

 lessened, other things being the same, the density of the lower half 

 will be greater or less, but its volume, and therefore its height, will 

 not be altered. For twice the quantity in the lower half will be 

 under twice the ])ressure from the upper half. 



3. If another gas with a different relative weight be substituted, 

 the height of the lower half will be inversely as the relative weight 

 — for the volume is so, other things being the same. 



4. If the force of gravity be different, the height of the lower 

 half will be inversely as that force — for the pressure is as the 

 force of gravity. 



5. If the temperature varies, the height of the lower half will be 

 directly as the absolute temperature. 



6. "When the gas is air, with relative weight 14'45, the 

 acceleration of gravity 32'2 feet in a second, and the temperature 

 0° Cent., the height of the lower half atmosphere is 3'44 miles, by 

 Maxwell's formula, wluch agrees with observation. It follows that 

 for any gaseous atmosphere round a spherical body, — • 



1445 32-2 T 586 T 



W ** G ''273'' ^''^= WG "°^ 

 W being the relative weight of the gas (hy drogen = 1) . 

 G, gravity in feet per second. 

 T, absolute temperatui'e in degrees Centigrade. 

 H, height of lower half of atmosphere in miles. 



7. The height of the upper half is indefinite, but its density at 

 any height is in known relation to the density at the bottom, the 

 gaseous laws holding good. At twenty times the height of the 

 lower half, the density is reduced to about one-millionth ; at forty 

 times to one-billionth. These are maximum densities at those 

 heights, unless the temperature above is greater than below. And 

 any substance of any probable density becomes inappreciable 

 when the density is reduced to one-bilUonth. It foUows that 

 5-86 T 



-~g-x40=the extreme height to which any appreciable attno 



sphere can be supposed to extend in miles. 



8. On this theory, if the sun has an atmosphere of hyib'ogcn 

 above the photosphere, its greatest height would be — 



at T = 0' Cent., 72 miles, 

 at T = 27,300° Cent., 7,200 miles, 

 at T = 273,000° Cent., 72,000 miles. 

 If a layer of hydrogen, resting on the photosphere, vanished at 

 a height of 5,000 miles, it would indicate a temperature of about 

 20,000° Cent. 



If the sun has an atmosphere appreciable at a height of one 

 million miles, the temperattu-e not exceeding 20,000' Cent., the gas 

 composing it, on the theory, must be at least 200 times lighter than 

 hydrogen. 



9. The height of the lower half of any atmosphere, on the above 

 theory, is nearly equal to half the height to which the mean 

 molecular velocity of the gas, at the mean temperature, would carry 

 a projectile upwards against gravity from the surface of the attract- 

 ing sphere. For it is so in the case of the earth's atmosphere, and 

 the relation must be constant, because the projectile height is as 

 the square of the velocity ; and the square of the mean molecular 

 velocity is, like the height of the half atmosphere, inversely as the 

 relative weight of the g:is and directly as the absolute temperature. 



The square of the molecular velocity of ail-, as determined dynami- 

 cally, at 0° Cent, is 2,526,000 feet per second. 



2,526,000 



2Ct = 64-4 ^ projectile height = 39,200 feet, 

 the half of which = 3'71 miles. The difference between this and 

 the estimated height, 3'4i miles, is not more than may bo due to 



errors in the fundamental data. But tii» reason for this particular 

 relation is not ai)parent. 



10. The decrease in gravity and temperature, and the increase 

 in superficial area in ascending, are not considered above. The 

 height of the lower half atmosphere is little affected by them, but 

 that of the upper half is incrcusod by the first and decreased by the 

 second and third ; and the effects of great disturbance by explosive 

 or other forces, as, for example, in the sun's atmosphere, have to be 

 considered separately. 



The assumption that no atmosphere is appreciable when reduced 

 to one-billionth of its density at the bottom is arbitrary, but the 

 limits of probable error from this source are not very wide. For 

 the reduction is carried to the million-billionth at a height of 

 sixty, and to the trillionth at that of eighty half atmospheres. 



The final results are necessarily approximations only. 



Albekt J. MOTT. 



WEATHER FORECASTS. 



[731]— Sir E. Beckett's communication on weather forecasts, 

 which you have reprinted from the Times, deserves some notice. 

 I reside in a district (the north of Ireland) in which, for reasons 

 well known to all meteorologists, the forecasts are much less 

 likely to prove accurate than those for the S.E. of England. Some 

 months ago it appeared to me that the Irish forecasts miL'ht be 

 made much more accurate, if the proper parties could be induced 

 to meet the needful expense, and, as a preliminary step, I set my- 

 self to carefully note the forecasts and their fulfilment under the 

 existing arrangements. I am now, therefore, able to subjoin an 

 analysis of the forecasts for the last four months of 1S.S2 for this 

 district. Space will not permit me to follow Sir E. Beckett's 

 method of giving each day in full, therefore the course I adopt is 

 this. I have records for fc8 days ; the forecasts which have turned 

 out quite correct I numbered 1. There were 34 of these, or equal 

 to 38i per cent. Those which were only partially correct I 

 numbered 2, which occurred on 33 days, or 374 per cent. Those 

 which were in great degree a failure I numbered 3 on 11 days, or 

 12^ per cent. No. 4, or total failures, were on 10 days, or Hi per 

 cent. 



Applying the same mode of analysis to the 24 days given by Sir 

 E. Beckett, I find a less favourable result. JTo. 1, according to my 

 valuation, occurred five times, or only 21 per cent. Xo. 2, nine 

 times, or 37 per cent. No. 3, four times, or 17 per cent. ; and 

 No. 4, six times, or 25 per cent. Of course, in making an analysis 

 like the above, where one has to deal with somewhat indefinite 

 terms, such as hot, cold, showery, fine, Ac, &c., a great allowance 

 has to bo made for the "personal equation" of the observer, but 

 allowing for that, it still appears to me that during the month chosen 

 by Sir E. Beckett, the forecasts were less snccessful than usual, 

 and are therefore hai-dh- fair to the Department. The value of 

 the forecasts is very different to different people, and I believe 

 many who, like myself, have a little knowledge, though quite 

 elementary, of meteorology, they have been of great service. For 

 my own part I should be very sorry to see them discontinued, and 

 would prefer that our efforts should be directed towards making 

 them more reliable, and therefore more useful, than in pooh-poohing 

 them altogether. F. W. Lockwood, Hon. Sec, B.N.F.C. 



THE GREAT COMET— MAGNETIC STORM. 



[732]— The Great Comet is still visible here to the naked eye in 

 Cauis Major. The tail, traceable for ten or twelve degrees, is of 

 about half the luminosity of the " Clouds of Magellan." 



On the night of January 8, from observations taken at the 

 Imperial Observatory, it was noticed that the nucleus presented an 

 elongated appearance, which was not the case on the previous 

 evening. With powers of 500 and 000. it was not only much 

 elongated, but subdivided into four small nebulosities, three of 

 which presented the appearance at the centres of stai-s of the 

 twelfth magnitude. In comparison with the others, the fourth 

 appeared less condensed, but a little more elongated. 



The observations were continued throughout the night, till 

 one o'clock a.m. (Rio de Janeiro time), when they were brought to 

 an abrupt termination by light cirrus, during which time no altera- 

 tion was discernible, but the four nuclei maintained their same 

 relative positions and aspects. The magnetic storm of November 

 was severely felt throughout the South American Continent, 

 though unaccompanied by the miracles which somehow have such 

 an affinity for our cousins of the stars and stripes. 



Rio de Janeiro, Jan. 10. T. H. D. 



STORED ENERGY. 



[733] — The following question may perhaps interest some of 

 your chemical readers, although I am not sure that it is original. 



